Three Dice Game

ABSTRACT

An apparatus and method for a three dice game of chance. A game surface is provided having discrete sections, each section including a plurality of numbers, e.g., four numbers from 3 to 18 obtained by the sum of a roll of three dice. The numbers have various payout odds, each section also having payout odds. A wager placed on a number in a particular section is paid off in accordance with the payout odds associated with that number. If the rolled sum does not correspond to that number but does correspond to another number in that section, wager is paid off in accordance with the payout odds of that section. In a particular embodiment, increased odds are given for rolling a hard way number wherein all three dice have the same number.

FIELD OF THE INVENTION

The invention relates to a dice game, in particular a game where players can place a variety of bets having various payouts depending on the outcome of the roll of three dice, and which is suitable for use in a casino.

BACKGROUND OF THE INVENTION

Players of games of skill and chance are constantly seeking games offering greater excitement and higher payouts. In an attempt to make games more exciting, various games have been invented that allow raising the wagers or providing a larger jackpot. For example, slot machines are often linked to one another, whereby the player of one machine who obtains a winning result receives a large jackpot based on the total play of the linked machines. A game that is fast and offers much player excitement is craps. This game involves the throwing of two dice. Unfortunately, the game is complex and difficult to learn, deterring many from playing it. Roulette offers simplicity but limited payouts a limited choice of types of bets, for example on the different colors, even or odds, and play on either single numbers or on groups of numbers with no compensation for losses.

A number of methods have been devised in an attempt to merge the excitement of dice throwing with a variety of payouts. U.S. Pat. No. 5,413,351 describes a dice game involving wagering on the outcome of a toss of three dice in which the player plays against a “dealer” and in which either the player or dealer has an opportunity to throw the dice a second time depending on whether the first throw resulted in a preselected combination of dice. U.S. Pat. No. 4,334,685 describes a three dice game with two white dice and a red die and in which betting rows have indicia designating certain fixed combinations and payouts as well as “any triple” and “any white double” sections with appropriate payouts. U.S. Pat. No. 3,761,091 is directed to the mechanics of a turntable for playing dice and describes a playing surface marked with various two dice combinations with various payouts. U.S. Pat. No. 6,601,848 describes a dice game with a game board displaying all the possible single roll dice combinations for from three to five dice and the payout odds for each of the possible single roll dice combinations. U.S. Patent Application No. 2005/0146092 (abandoned) describes a three dice game where the game board displays discrete regions associated with pre-valued odds, including number bets, line bets, and split pair bets, but does not provide for a player having a bet on a number to win if the number is not itself thrown.

BRIEF SUMMARY OF THE INVENTION

The present invention provides a three dice game and method of play that provides a higher level of interest and excitement than provided by current or prior methods of dice play or roulette play. The three dice game uses discrete sections. Each section includes a plurality of numbers, each number representing the sum of a roll of three dice. Together, the sections represent all the various possible three dice roll sums. A wager placed on a number in a particular section is paid off in accordance with payout odds associated with that number. In accordance with an embodiment of this invention, if the rolled sum does not correspond to that number but does corresponds to another number in that section, the wager is paid off in accordance with the payout odds for that section. Accordingly, in this embodiment, if a player losses his or her wager on a particular number, as long as the sum of roll of dice is equal to another number in that section, the player will be awarded with the payoff in that section. The section payoff can be set so as to be a push or to be a small plus reward, e.g., 1½:1 or 2:1.

In particular embodiments, there are four sections, each with four numbers representing all 16 of the possible sums of a three dice roll. In a specific embodiment, the distribution of numbers in the sections is such that the odds of rolling a number that falls one of three sections are approximately the same for each such section. The odds of rolling a number that falls in the remaining section is significantly higher than for the first group of sections. In very specific embodiment, sections in the first group of sections respectively contains (a) the numbers 5, 7, 10, and 13, (b) 6, 9, 12 and 15, and (c) 8, 11, 14, and 16. The remaining section contains the numbers 3, 4, 17, and 18.

In a further embodiment of the invention, increased odds are given for rolling a hard way number wherein all three dice have the same number. In the embodiment in which one of the sections contains the numbers 6, 9, 12 and 15, each of the numbers in that section can be rolled a hard way, that is, respectively, 222, 333, 444, and 555. In the section containing the numbers 3, 4, 17, and 18, only the numbers 3 and 18 can be obtained the hard way, i.e., by 111 or 666. The payoff odds for the winning numbers will be lower to enable the higher payoff for a hard way roll of the three dice.

BRIEF DESCRIPTION OF THE DRAWING

For a more complete understanding of the present invention, reference is now made to the following descriptions taken in conjunction with the accompanying drawing, in which:

FIG. 1 is a casino table layout for use in practicing the invention with a hard way wager separately shown and where odds wherein the payout to a player is approximately 85% of the actual odds; and

FIG. 2 is a casino table layout for use in practicing the invention with incorporated hard way odds wherein the payout to a player is approximately 85% of the actual odds.

DETAILED DESCRIPTION OF THE INVENTION

The odds offered to a player will depend on the percentage of the actual odds that a casino is willing to give to the player and on the number of payout opportunities available to the player, for example, whether or not a hard way payout is available. These odds are distinctly different for the present invention than they are for other three dice games because of the consolation awarded if the number chosen by a player is not rolled but the rolled number falls in the same section. Straight number odds with no consolation award are well known, for example as found Table 1 of U.S. Pat. No. 6,601,848. There, the actual odds of rolling a particular number with from two to five dice are given by the formula: P=Y(X−W_(n))/W_(n), where P represents the payout, X represents the total number of possible combinations for a given number, W_(n) represents the number of winning numbers per X rolls of the dice, and y represents the payout percentage (i.e., 1−Y is the house advantage). With three dice the formula becomes P_(n)=Y(216−W_(n))/W_(n). Table 1 provides the following actual odds with Y=100%):

TABLE 1 [P_(n) = (216 − W_(n))/W_(n)] Roll W_(n) Odds (:1) 3 1 215 4 3 71 5 6 35 6 10 20.6 7 15 13.4 8 21 9.3 9 25 7.6 10 27 7 11 27 7 12 25 7.6 13 21 9.3 14 15 13.4 15 10 20.6 16 6 35 17 3 71 18 1 215

However, the above formula does not contemplate any consolation award. As described in the Summary of the Invention, each section includes a plurality of numbers, each number representing the sum of a roll of three dice. Together, the sections represent all the various possible three dice roll sums. A wager placed on a number in a particular section is paid off in accordance with payout odds associated with that number, but if the rolled sum does not correspond to that number but does corresponds to another number in that section, the wager is paid off in accordance with the payout odds for that section. The odds for a section depends on which numbers are chosen to be together in the section. The formula for determining those odds is P=Y(216−W_(s))/W_(s), where W_(s) represents the number of winning numbers in the section per X rolls of the dice (and P and Y are as before).

In accordance with a specific embodiment of the invention, there are four sections and the numbers chosen to be placed in particular section are chosen so that three of the sections have approximately the same odds, which is accomplished if a first group of three sections respectively contains the numbers (a) 5, 7, 10, and 13, (b) 6, 9, 12 and 15, and (c) 8, 11, 14, and 16. The remaining section contains the numbers 3, 4, 17 and 18. Take the example of a section having the numbers 6, 9, 12 and 15, the odds for having a number in that section can be calculated by adding the individual odds for the numbers in that section as “W_(s)’ in the formula. For 6, W_(n)=10, for 9, W_(n)=25, for 12, W_(n)=25, for 15, W_(n)=10. The total number of winning bets per 216 rolls of the dice is 70, so the odds for the section is (216−W_(s))/W_(s) or 2.0857, rounding to 2.1. Table 2 provides the actual section odds with Y=100%.

TABLE 2 [P_(s) = (216 − W_(s))/W_(s)] Actual Section Nos. W_(s) Odds (:1) 5, 7, 10, 13 69 2.1 6, 9, 12, 15 70 2.1 8, 11, 14, 16 69 2.1 3, 4, 17, 18 8 26

Assuming the player places a bet on number 6, he would win if a 6 is rolled, but he would also win if a 9, 12 or 15 is rolled. To calculate the odds with a consolation award, an adjustment must be made to compensate for the consolation award. This can be done by treating the consolation award as if it were a separate wager. The player would receive a payout based on selecting the winning roll and would also receive a payout on the separate wager for that section. The awards are added up and since there are two wagers, the payout for a winning number is divided by two. As an example (for purposes of calculation assuming there is no hard way award and that the casino pays out 100%), if the number selected is 6, the section has the numbers 6, 9, 12 and 15. The total odds are obtained by adding the odds for the single number wager (from Table 1) and the section wager (from Table 2) and dividing by the number of wagers, which is 2. In the case of rolling a 6, the payout odds are 20.6 (for the 6) and 2.1 (for the section) for a total of 22.7 for two wagers. The payout would then be 22.7/2=11.35:1 for the number 6. If the rolled number is not 6, but instead is 9, 12 or 15, then the payout would be 2.1 divided by two wagers=1.05:1. The formula is P_(n+s)=(216−W_(n))/2W_(n))+(216−W_(s))/2W_(s)), which can be expressed as P_(n+s)=(P_(n)+P_(s))/2. Table 3 provides the payouts for each winning number, with Y=100%, and also with a house percentage of 15%, i.e., Y=0.85:

TABLE 3 Winning Number Odds With Consolation Award (P_(n+s) = (P_(n) + P_(s))/2) Actual 85% Payout Roll Odds (:1) Odds (:1) 3 120.5 102.4 4 48.5 41.2 5 18.55 15.8 6 11.35 9.6 7 7.75 6.6 8 5.7 4.8 9 4.85 4.1 10 4.55 3.9 11 4.55 3.9 12 4.85 4.1 13 5.7 4.8 14 7.75 6.6 15 11.35 9.6 16 18.55 15.8 17 48.5 41.2 18 120.5 102.4

Table 4 provides the payouts for each section in the first group (where there is no winning number) number, with Y=100%, and also with a house percentage of 15% where Y=0.85:

TABLE 4 Section Odds As Consolation Award (P_(s))/2) Actual 85% Payout Section Nos. Odds (:1) Odds (:1) 5, 7, 10, 13 1.05 0.89 6, 9, 12, 15 1.05 0.89 8, 11, 14, 16 1.05 0.89 3, 4, 17, 18 13 11

In a particular embodiment, the casino wants to adjust the section payout odds for the consolation awards to be a push (odds of 1:1) for what has been referred to above as the first group of sections (i.e., for sections with respective numbers (a) 5, 7, 10, and 13, (b) 6, 9, 12 and 15, and (c) 8, 11. 14). In that case, the odds for the selected number would need to be adjusted to retain the house percentage. In the example, to adjust the 0.89:1 (85%) payout to 1:1, one simply has to make the wager on section (a), (b) and (c) such that it pays 1:1, which can be done by dividing 1 by 0.89, which equals 1.12 so that the wager for the section becomes $1.12 (assuming a basic wager of $1.00. The payout for the remaining section (3, 4, 17, 18) would also increase from 11:1 to 12.3:1 (P_(s)=(216−W_(s))/2.12W_(s)), but the payout (with the house 15% percentage) for the winning number would decrease because the total wager would then be $2.12. This results in dividing the number payout by 2.12 instead of by 2, i.e., P_(n+s)(P_(n)+1)/2.12. For the remaining section (3, 4, 17 and 18), the payout is P_(n+s)=(P_(n)+12)/2.12 is Tables 5 and 6 respectively give the winning number odds and the section odds, each with a house percentage of 15%.

TABLE 5 Winning Number Odds With Push Consolation Award (P_(n+s) = (P_(n) + P_(s))/2.12) Actual 85% Payout Roll Odds (:1) Odds (:1) 3 107.5 91.4 4 39.1 33.2 5 17 14.4 6 10.2 8.7 7 6.8 5.8 8 4.9 4.1 9 4.1 3.4 10 3.8 3.2 11 3.8 3.2 12 4.1 3.4 13 4.9 4.1 14 6.8 5.8 15 10.2 8.7 16 17 14.4 17 39.1 33.2 18 107.5 91.4

Table 6 provides the push odds and payouts for each section in the first group (where there is no winning number) number, with Y=100%, and also with a house percentage where Y=0.85:

TABLE 6 Section Payouts when First Group Of Sections Are Each A Push (1.12P_(s)) Actual 85% Payout Section Nos. Odds (:1) Odds (:1) 5, 7, 10, 13 1.18 1 6, 9, 12, 15 1.18 1 8, 11, 14, 16 1.18 1 3, 4, 17, 18 14.6 12.4

Table 7 provides the table odds for each number and consolation award for the respective section, based on the 85% winning number odds from Table 5 and the section payout odds from Table 6, each reduced to a convenient lower whole number.

TABLE 7 Rounded Winning Number Odds With Push And 85% House Percentage Number Payout Section Payout Roll Odds (:1) Odds (:1) 3 91 12 4 33 12 5 14 1 6 8 1 7 5 1 8 4 1 9 3 1 10 3 1 11 3 1 12 3 1 13 4 1 14 5 1 15 8 1 16 14 1 17 33 12 18 91 12

FIG. 1 shows a casino table layout based on Table 7.

In accordance with a further embodiment of the invention, increased odds are given for rolling a hard way number wherein all three dice have the same number. In the embodiment in which one of the sections contains the numbers 6, 9, 12 and 15, each of the numbers in that section can be rolled a hard way, that is, respectively, 222, 333, 444, and 555. In the section containing the numbers 3, 4, 17, and 18, only the numbers 3 and 18 can be obtained the hard way, i.e., by 111 or 666. There are alternative ways in which a hard way payout can be obtained. In one way, the board layout has a hard way box on which a separate wager can be placed. The actual odds for such a wager is given by P=Y(216−W_(h))/W_(h), where W_(h) represents the number of winning numbers per 216 rolls of the dice Since there are six ways that a hard way wager can be won, the actual odds, P_(h), for such a wager is (216−8)/8=26:1=. At a house percentage of 15%, the provided odds are 22.1:1, which can be rounded down to 20:1, as shown in FIG. 1.

Another way to provide hard way odds is to include it in the original wager. This can be calculated in a way similar to the way the consolation award was calculated, by considering the hard way as a third wager for those numbers that have a hard way and integrating it into the odds. Such a calculation need be made only for the four numbers that can have a non-hard way throw, which would be 6, 9, 12. and 15. For example a throw of 6 can be made nine ways in addition to the hardway of 666. That would be 114, 141, 411, 123, 132, 321, 213, 231 and 321. No recalculation need be done for 3 and 18 because they can only be thrown with 111 and 666, respectively. We need to divide the odds for each of the four numbers 6, 9, 12 and 15 by 3.12 (one wager for the number, 1.2 wagers for the section—to enable the push—and one wager for the hard way). Since a separate hardway payout is provided, the payout for a number having a hard way is given by P_(n+s+h)=(P_(n)+P_(s))/3.12. Since the numbers 6, 9, 12 and 15 are in a push section, the formula for those numbers can be reduced to P_(n+s+h)=(P_(n)+1)/3.12. The results are given in Table 8:

TABLE 8 Odds For Numbers Having A Push And A Hard Way [P_(n+s+h) = (P_(n) + 1)/3.12] Section Payout 85% of Roll Odds (:1) Odds (:1) Odds (:1) 6 1 6.9 5.9 9 1 2.8 2.3 12 1 2.8 2.3 15 1 6.9 5.9

Numbers 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17 and 18 have the odds shown in Table 7. Table 9 provides the table odds for each number and consolation award for the respective section, based on a 85% house percentage, each reduced or raised to a convenient lower whole number

TABLE 9 Rounded Number Odds With Push, Hard Number, And 85% House Percentage Non-Hard Hard Number Payout Section Payout Payout Roll Odds (:1) Odds (:1) Odds (:1) 3 86 12 — 4 33 12 — 5 14 1 — 6 6 1 20 7 5 1 — 8 4 1 — 9 2 1 20 10 3 1 — 11 3 1 — 12 2 1 20 13 4 1 — 14 5 1 — 15 6 1 20 16 14 1 — 17 33 12 — 18 86 12 —

FIG. 2 shows a casino table layout based on Table 9.

The odds actually offered by a casino may be different from those calculated for FIGS. 1 or FIG. 2, based on whether the casino uses a higher or lower house percentage and its method of rounding out the odds, i.e., whether the casino chooses to reduce its percentages by rounding up some or all of the numbers. It will be appreciated that the casino can set whatever percentages it wants using the methods of calculation set out above, or their own calculations. The game could also be played electronically, like poker slot machines. In the Figures, to provide more interest, the sections have been given city names, which need not be used or any other names can be chosen. The sections in which a push is provided are named Los Angeles, New York and Washington D.C., and the remaining section is named Las Vegas.

Although the present invention has been described in connection with the preferred embodiments, it is to be understood that modifications and variations may be utilized without departing from the principles and scope of the invention, as those skilled in the art will readily understand. Accordingly, such modifications may be practiced within the scope of the following claims. 

1. A game of chance device, comprising: a game surface comprising discrete sections, each section including a plurality of preselected numbers, each number representing the sum of a roll of three dice, the totality of the preselected numbers representing all the various possible three dice roll sums, each number having preselected payout odds associated with the roll of a three dice sum corresponding to the number, and each section having preselected payout odds associated with the section for the roll of a three dice sum corresponding to one of the numbers in that section, whereby (a) a wager placed on a number in a particular section is paid off in accordance with the payout odds associated with that number if upon a roll of the three dice a sum is obtained that corresponds to that number, and (b) if the said rolled sum does not correspond to that number but does correspond to another number in that section, said wager is paid off in accordance with the preselected payout odds of that section.
 2. The game of chance of claim 1 in which there are equal amounts of preselected numbers in each section.
 3. The game of chance of claim 1 in which there is a group of sections and a remaining section, the odds of rolling a number that falls in one of the group of sections are approximately the same for each section in the group, and the odds of rolling a number that falls in the remaining section is significantly higher.
 4. The game of chance of claim 3 in which each of the numbers in one of the section in the group can be obtained by a hard way roll wherein all three dice have the same number, which can be wagered on automatically, or a separate wager can be placed on a hard way bet.
 5. The game of chance of claim 3 in which there are four sections and four numbers in each section.
 6. The game of chance of claim 5 in which one section of the first group of sections contains the preselected numbers 5, 7, 10, and 13, a second section of the first group of sections contains the preselected numbers 6, 9, 12 and 15, and a third section of the first group of sections contains the preselected numbers
 8. 11. 14, and 16, and said remaining section contains the preselected numbers 3, 4, 17, and
 18. 7. A game of chance device, comprising: a game surface comprising four discrete sections, each section including four preselected numbers, each number representing the sum of a roll of three dice, the totality of the preselected numbers representing all the various possible three dice roll sums, each number having preselected payout odds associated with the roll of a three dice sum corresponding to the number, and each section having preselected payout odds associated with the section for the roll of a three dice sum corresponding to one of the numbers in that section, whereby (a) a wager placed on a number in a particular section is paid off in accordance with the payout odds associated with that number if upon a roll of the three dice a sum is obtained that corresponds to that number, and (b) if the said rolled sum does not correspond to that number but does correspond to another number in that section, said wager is paid off in accordance with the preselected payout odds of that section.
 8. The game of chance of claim 7 in which all of the numbers in one of the section can be obtained by a hard way roll wherein all three dice have the same number.
 9. The game of chance of claim 7 in which one of the sections contains the preselected numbers 5, 7, 10, and 13, a second section contains the preselected numbers 6, 9, 12 and 15, a third section contains the preselected numbers
 8. 11. 14, and 16, and the remaining section contains the preselected numbers 3, 4, 17, and
 18. 10. A method of playing a dice game comprising the steps of providing a set of three identical standard dice; providing a wagering device comprising a game surface having discrete sections, each section including a plurality of preselected numbers, each number representing the sum of a roll of three dice, the totality of the preselected numbers representing all the various possible three dice roll sums; associating preselected payout odds with the roll of a three dice sum corresponding to the number; associating payout odds with each section the roll of a three dice sum corresponding to one of the numbers in that section; arranging for the three dice to be rolled; paying the payout odds to any player who has placed a wager on a number in a particular section in accordance with the payout odds associated with that number if upon the roll of the three dice a sum is obtained that corresponds to that number, and if the said rolled sum does not correspond to that number but does correspond to another number in that section, then paying the payout odds of that section.
 11. The method claim 10 in which there are equal amounts of preselected numbers in each section.
 12. The method of claim 10 in which there is a group of sections and a remaining section, the odds of rolling a number that falls in one of the group of sections are approximately the same for each section in the group, and the odds of rolling a number that falls in the remaining section is significantly higher.
 13. The method claim 12 in which the odds of rolling a number that falls in any one of the first group of sections is approximately the same as the odds of rolling a number that falls in any other of the first group of sections.
 14. The method of claim 10 in which there are four sections and four numbers in each section.
 15. The method of claim 14 in which one of the sections contains the preselected numbers 5, 7, 10, and 13, a second section contains the preselected numbers 6, 9, 12 and 15, a third section contains the preselected numbers
 8. 11. 14, and 16, and the remaining section contains the preselected numbers 3, 4, 17, and
 18. 16. A method of playing a dice game comprising the steps of providing a set of three identical standard dice; providing a betting device comprising a game surface having four discrete sections, each section including four preselected numbers, each number representing the sum of a roll of three dice, the totality of the preselected numbers representing all the various possible three dice roll sums; associating preselected payout odds with the roll of a three dice sum corresponding to the number; associating preselected section payoff odds with the roll of a three dice sum corresponding to any one of the numbers in a respective section arranging for the three dice to be rolled; paying the payout odds to any player who has placed a wager on a number in a particular section in accordance with the payout odds associated with that number if upon the roll of the three dice a sum is obtained that corresponds to that number, and if the said rolled sum does not correspond to that number but does correspond to another number in that section, then paying the payout odds of that section.
 17. The game of chance of claim 16 in which one or more of the numbers in a section can be obtained by a hard way roll wherein all three dice have the same number.
 18. The method of claim 16 in which one of the sections contains the preselected numbers 5, 7, 10, and 13, a second section contains the preselected numbers 6, 9, 12 and 15, a third section contains the preselected numbers
 8. 11. 14, and 16, and the remaining section contains the preselected numbers 3, 4, 17, and
 18. 